Truss structures can be used in vehicles, such as aircraft, boats, trucks, and buses to support loads or structures in a vehicle. For example, a truss supported by frame members in an aircraft may support lavatories, galleys, overhead storage bins, partitions, and other monuments. The trusses include various truss tie rods to support the structure(s), including vertical tie rods that support the weight of the structure(s), lateral tie rods that support lateral loads on the structure(s), and diagonal tie rods that support forward and aft loads on the structure(s). In various instances, a truss structure could impart loads into the structure of a vehicle. For example, an airframe of an aircraft may be designed to flex when it encounters turbulence. However, a truss that is connected to the airframe could prevent or inhibit such flexing.